I have not tested this build in normal. This build was generated through Dominion only. Use at your own risk in normal. Alot of people may find this build odd for Kat. However I am heavy dominion player and strive to find the best builds. Builds will always have alterations depending on who your playing. So don't fallow builds how they say 100% every game. You must adjust to what you are playing.~~~~
Ap kat is nice. however. her ult is easy to interrupt. sec that happens. your dead. and if you look at her skills. she doesnt get **** of ap + to her skills from her actual AP. kinda like wasting alot of money. spell penetration would be better. or be like me and just go for tankier.
my build > greater > greater than> Ap kat
thats how much more effective this is.couple undefeated match histories. So far this build im around 35 wins to 3 loss's with 90% games solo Q.

simple. after using will of the ancients as my second item on my build for awhile i discovered.... its useless. The little amount of life tap you receive is not worth how much def u can add. IF anything it can be one ur last items. witch there should be a Extremely rare chance that u make it to the 6th item.

These runes are set up for magic pen and Armor def. You could also do magic def if you wish. i find runes to be useless honestly. They don't do enough to make them worth it. So use what u want, this is what I use. I throw in a crit change rune. better to have least some chacne to crit.

It is what it is. Cant really change it to be better. u could learn honor Guard instead of moving speed. But 1.5% of 100 damage is 1.5 damage. u do the math. is it worth it? or would u like to chase someone faster.

lately ive been building abysell second do it gives magic resist and magic pend and ap. witch is what u want. and 99% time they have more ap than ad def.
OK and here is the important part. This can change depending on how you play. You must adjust to who u play.
First off.
I start with Spell penetration boots. Always. ---- if u would like u can start with Cd boots. However i do not find them useful, do to her passive. I also buy 4 Hp pots
Second.
I look at their team. this is were u determine if there more ap or more ad or whats gonna burst u to death. This is were u choose between Force first or Thorn first. Lots of ap, go with Force. Lots of Ad, go for Thorn. If they have a even amount. I normally buy the 700 armor and the 740 magic resist at same time, than see what I have the most problems with, and decide from there.
3rd.
Unless you are facing pure ap or pure ad you than build w.e armor you didnt build first now.
4th. I Than go for rylais. ap,hp,slow why wouldn't u want it? just dont want it to soon when its not as useful.
5th. (removed Deathcap) Dont pay out, with the price of it this late in the game. I normally start building void staff. Unless theres no magic def on their team. Fat Chance. If There Isn't, than I skip to number 6.
6th. the rare chance ull ever be in a match this long. this is what u get. Zhonya's or Will of the ancients.
at this point you should be good to go. be careful i tend to rack up deaths from taking on 1v3 to much lol. when u can take 3 people down its tempting every time u see it XD
to be honest once you get the first 3 items. you can build w.e order u need for the rest. any works good.

Learn 1 of each to start u off.
master Shunpo as fast as u cant/excluding ult
after that master bouncing blade
than after that master kill instincts.
Level up Death Lotus every time u can.

Heal. Heal is one the best underrated skills in this game. The game buffed it to make it better. fine by me. Heal is used for baiting ,surviving, and aiding your team. people tend to atk u at low life thinking they can kill u. however u turn heal on bust ur ult out and bam tables turned. Ghost is ghost. Dont have it? than your dumb. best dominion skill.
try to save your heal for when its needed. dont use it like a idiot just to heal u for no reason.

U dont farm minions. U stopp them. U farm off the other teams players.

Pros
Burst
Carry
Tanky
Fast cooldowns
//////////////////
Cons
squishy till you get your gear.
Even after you have your gear you will remain top targeted.
Easily shut down by Alistar, or Vollibear
Your ult must be timed perfect! to easy to cancel it.

Start off by running to your top, closest. ( Not bottom Turret.) start capping that. once you have capped it. Cast ghost and meet up with your team up top. Start pinging people to kill. Start burning ur skills on low life people or save for ks. by time top has been dealt with. you begin the armor. and grabs some pots. rush to mid grab buff. your ult should b up. this is were, you make a choice: kill bot or save top. or do both. from here on out its up to u, go to bases kill them off take the base get your gear, this build will allow u to suck up lots of hits while hitting your ult as long as u dont miss when u fire it. most damage from her will come from leveling up your moves. witch is plunty, idk u can give it a try.